A Data-Driven Model for Wind Plant Power Optimization by Yaw Control

Transcription

1 4 American Control Conference (ACC) June 4-, 4. Portland, Oregon, USA A Data-Driven Model for Wind Plant Power Optimization by Yaw Control P. M. O. Gebraad, F. W. Teeuwisse, J. W. van Wingerden, P. A. Fleming, S. D. Ruben, J. R. Marden, and L. Y. Pao Abstract This paper presents a novel parametric model that will be used to optimize the yaw settings of wind turbines in a wind plant for improved electrical energy production of the whole wind plant. The model predicts the effective steady-state flow velocities at each turbine, as well as the resulting electrical energy productions, as a function of the axial induction and the yaw angle of the different rotors. The model has a limited number of parameters that are estimated based on data. Moreover, it is shown how this model can be used to optimize the yaw settings using a game-theoretic approach. In a case study we demonstrate that our novel parametric model fits the data generated by a high-fidelity computational fluid dynamics model of a small wind plant, and that the data-driven yaw optimization control has great potential to increase the wind plant s electrical energy production. I. INTRODUCTION Each wind turbine in a wind plant influences the electrical energy production and loads of other turbines through wakes of slow-moving, turbulent air that form downstream of the turbine s rotor. If another turbine is standing in the path of a wake that has not fully recovered to free-stream conditions, the reduced wind speed in this wake results in a lower electrical energy production. The amount of wake interaction depends on time-varying atmospheric conditions (e.g., wind speed, turbulence, atmospheric stability, and wind ), and on the operating point of each turbine (rotor speed, pitch angles of the blades, and yaw angle) that can be adjusted by changing the control settings of each turbine. The goal of this paper is to develop an internal model for a wind plant controller. The internal model predicts the impact of control settings on the steady-state wake interaction effects in the wind plant. The wind plant controller can use this model to increase the wind plant s electrical energy production through model-based optimization of the control settings. Previous work has mainly aimed at reducing wake interaction by adjusting the axial induction of turbines to improve wind plant performance, which can be achieved by adjusting pitch and torque. This concept was first proposed P.M.O. Gebraad, F.W. Teeuwisse, and J.W. van Wingerden (j.w.vanwingerden@tudelft.nl) are with the Delft Center for Systems and Control, Delft University of Technology. Their work is supported by the Far Large Offshore Wind (FLOW) project no. Offshore wind power plant control for minimal loading and by the NWO Veni Grant no. 9 Reconfigurable floating wind farm. P.A. Fleming is with the National Renewable Energy Laboratory (NREL). NREL s contributions to this report were funded by the Wind and Water Power Program, Office of Energy Efficiency and Renewable Energy of the U.S. Department of Energy under contract No. DE-AC-5CH. The authors are solely responsible for any omission or errors contained herein. S.D. Ruben, J.R. Marden, and L.Y. Pao are with the University of Colorado, Boulder. in [], and more recently model-based static optimization strategies were tested in [] [4], and model-based control algorithms [5] [8], as well as data-driven model-free control algorithms [9], [] have been proposed for performing the optimization. In this work, we use the yaw degree of freedom of the wind turbine to deflect the wake of turbines away from downstream turbines, which was shown to have great potential in high-fidelity simulations in [], []. The concept was also tested in a small wind plant in []. These tests confirmed that the wake can be redirected using yaw, but because only a limited amount of data could be gathered, no quantitative analysis could be made. High-fidelity models, based on a coupling of detailed turbine dynamics models with accurate wind flow models, such as computational fluid dynamics (CFD)-based models [4] [], have an important role in wind plant controls development, as they allow the algorithms to be tested in a controlled environment. However, because of their computational complexity, they are less suited as internal models. Therefore, we aimed to develop a novel simplified parametric model for which the parameters can be identified using turbine power measurements. In this paper, a high-fidelity CFD wind plant model was used to develop the simplified parametric model. Next, that parametric model was employed for model-based optimization of the yaw settings in a wind plant using a game-theoretic approach, and finally these model-predictive-optimized settings were validated in a highfidelity wind plant simulation. The low number of parameters in the simplified parametric model allow it to be tuned online, based on real-time turbine power measurements, in order to adapt to changing atmospheric conditions. Previous work on yaw optimization algorithms for wind plants [7] did not include validation of the optimized settings using highfidelity numerical simulations. The rest of this paper is organized as follows. The experiments performed in the high-fidelity CFD simulator to obtain identification data for the parametric model are described in more detail in Section II. The simplified parametric model is presented in Section III. Section IV presents the game-theoretic approach to calculate optimal yaw control settings based on the simplified model. Finally, in Section V, a simulation study is presented to validate these modelpredictive optimized settings in a high-fidelity wind plant simulation /$. 4 AACC 8

2 II. EXPERIMENTS IN SOWFA, A HIGH-FIDELITY CFD WIND PLANT SIMULATOR The Simulator for On/Offshore Wind Farm Applications (SOWFA) is a CFD simulator of the three-dimensional wind flow around one or more turbine rotors in the atmospheric boundary layer. The rotating rotor blades are modeled through an actuator line approach [8]. The actuator lines are coupled with the FAST turbine aeroelastics simulator [9] that calculates the loads, power, and rotor speed of each turbine, in addition to the forces that each turbine blade exerts on the flow. Each turbine can be controlled using an individual control algorithm implemented in FAST, but also through a plant-wide supervisory or distributed controller. SOWFA was developed at the National Renewable Energy Laboratory (NREL), see [], [], and [] for more details. In [], [], SOWFA simulation results were presented that show: ) how effective the yaw techniques are at wake re, ) what the effect of the yaw wake re techniques is on the electrical energy production and loads of downstream turbines that are standing in the wake of the yawing turbine, and ) the effect of repositioning a turbine from full wake to partial wake on electrical energy production and loads. More in particular, in [], experiments are described with a setup of two NREL 5-MW baseline turbines [] that are aligned in the wind with a downwind spacing of 7 rotor diameters (7D). The simulated turbulent inflow has a mean hub-height free-stream wind speed U of 8 m/s and a turbulence intensity of %. The data of the following two experiments performed in [] are used in this paper (cf. Figure a). In Experiment, the upstream turbine (T) is yawed to redirect its wake away from the downwind turbine (T), resulting in an energy production decrease for T, but an energy production increase for T; in Experiment, T is moved in the cross-wind to reduce the overlap of its rotor with the wake of T. See Figure b for the time-averaged power data from these experiments. SOWFA high-fidelity CFD simulations are typically run for a few days on a cluster with a few hundred processors [], []. Because of the complexity and computational costs of the SOWFA model, it is not suitable as an internal model for a wind plant controller. However, the data generated by SOWFA can be used to develop simplified models that can be directly used by the controller. In Section III, we describe how the power data from Experiments and are used to identify such a simplified control-oriented model. In Section V, SOWFA is used to evaluate the control techniques based on the simplified model in a high-fidelity simulation. III. A DATA-DRIVEN PARAMETRIC WIND PLANT MODEL The model presented here is a combination of the Jensen model [], [4], combined with a model for wake deflection through yaw [5]. Further, we augment the model to be able to empirically fit it with the power measurements obtained in the Experiments and..5 x.5.5 Experiment Experiment U γ 7D T {a, γ } Experiment T Turbine, SOWFA results Turbine, SOWFA results Total, SOWFA results Parametric model {a, γ } U T 7D Y {a, γ } (a) Experimental setups Yaw angle turbine, γ [deg].5 x.5.5 (b) Time-averaged power data T {a, γ } Experiment Lateral position turbine, Y [m] Fig. : SOWFA simulation setup and results for Experiments and, cf. Section II. We used the power data to find the parameters of the control-oriented model, cf. Section III. A. Turbine power Let F = {,,,N} denote a set of indices that number the wind turbines in a wind plant, with N denoting the total number of turbines. When the effective wind speed at a turbine j, denoted as U j, is known, the steady-state power of each turbine is calculated as []: P j = ρa jc P (a j,γ j )U j j F () where ρ is the air density, A j is the rotor area, and C P is the power coefficient of the turbine. In nonyawed idealized conditions, the power coefficient is related to the axial induction factor of each turbine, defined as a j = U j,d /U j with U j,d being the wind speed at the rotor, and U j the free-stream wind speed in front of turbine j, as C P (a j ) = 4a j [ a j ], []. In the model presented here, we applied a correction to this relationship to account for the effect of the yaw misalignment angle γ j on the rotor power coefficient, following the example of the experimental studies in [7]. Further, we used a constant scaling of the C P value, η, to account for other losses and match the maximum C P =.48 value for the NREL 5-MW turbines reported in []. This resulted in: C P (a j,γ j ) = 4a j [ a j ] ηcos(γ j ) p P. () While [7] found a parameter value p P = to fit data from wind tunnel tests, the parameters settings listed in Table I were found to fit the yaw-power plot of the upstream turbine (T) in SOWFA Experiment, see Figure b, assuming an idealized axial induction of a j = /. In the remainder of this section, we describe how the effective wind speeds U j at each turbine are estimated by the model, using a model for steady-state wake behavior. 9

3 U j turbine j F D,x F D FD,y γ j D w, j, D w, j, D w, j, U j Ai,j, ol Ai,j, ol Ai,j, ol ξ j Near wake Far wake Mixing zone y x U j turbine j (a) Top view (b) Cut-through at downstream turbine Fig. : The three different wake zones of the parametric model. The areas overlapping with a downstream rotor j, A ol i, j,q, are used to calculate the effective wind speed at turbine j. wake turb. power deflection expansion velocity η.77 k d.5 k e.5 M U,.5 a U 5 p P.88 a d -4.5 m e, -.5 M U, b U. b d -. m e,. M U, 5.5 m e, B. Wake deflection TABLE I: parametric model parameters Yawing a turbine rotor causes the thrust force that the rotor exerts on the flow, F D, to rotate in such a way that a cross-wind component is induced [5], cf. Figure a, which causes the wind flow to deflect in the opposite of the yaw rotation. Because the wake deflection is induced by the thrust force, the yaw deflection is a function of the thrust coefficient of the turbine C T = F D /(ρa j Uj ), which for nonyawed conditions can be related to the axial induction factor a j of the rotor, as follows []: C T (a j ) = 4a j [ a j ]. () The following relationship between the yaw angle of a turbine j and the angle of the centerline of its wake, ξ j, was derived in [5]: with: ξ j (x) C T (a j,γ j ) ( + k d x/d) (4) C T (a j,γ j ) = cos (γ j )sin(γ j )C T (a j ) (5) where x is the axial distance from the rotor, D is the rotor diameter of the turbine, and k d is a model parameter that defines the sensitivity of the wake deflection to yaw. By integrating the tangent of the wake centerline angle over x, the yaw-induced lateral offset of the wake center with respect to the hub of turbine j, denoted as y w,yaw, j, can be found: x y w,yaw, j (x) tan(ξ j (x))dx. () This integral can be approximated by integrating the second order Taylor series approximation of ξ (x), yielding: [ ] ] 4 C T (a j,γ j ) 5[ xkd D + + C T (a j,γ j ) x y w,yaw, j (x) [ ] 5 k d xkd D D +. (7) Further, in the experiments described in [], it was found that a small lateral wake deflection occurs when the turbine is not yawed (i.e., γ j = ). This deflection can be explained by vertical shear in the boundary layer and wake rotation: in reaction to a rotor rotating clockwise, low-speed flow in the lower part of the boundary layer will be rotated up and to the right, and high-speed flow in the upper part of the boundary layer will be rotated down and to the left, and as a result the wake deflects to the right. Because in Experiments and the wake behavior was tested for a single mean wind velocity with a limited velocity variance caused by turbulence, the exact dependence of the wake deflection on rotor speed could not be derived from the power data obtained. Therefore, this rotation-induced wake lateral offset was parametrized through a simple linear function: y w,rotation (x) = a d + b d x. (8) Combining the rotation-induced and yaw-induced components, the lateral position of the wake center with respect to the hub of a turbine j is given by: C. Wake expansion y w, j (x) = y w,rotation (x) + y w,yaw, j (x). (9) In its original form, the Jensen model [], [4] assumes a wake that is expanding proportionally to the axial downstream distance from the rotor, and a wind velocity in the wake that is uniform in the lateral. In this work we extend the model to better match the data from Experiment and by dividing the wake in three areas that also expand proportionally with the distance to the rotor, but each with their own expansion factor (see Figure a). The diameters of the wake areas behind a turbine j are given by: D w, j,q (x) = max(d j + k e m e,q x,) ()

4 with index q =,, numbering the different areas, D j being the rotor diameter of turbine j, and with parameters m e,q, k e being coefficients defining the expansion of the areas. The different wake areas can be referred to as the near wake (q = ), far wake (q = ), and mixing zone (q = ), in accordance with the terms that are commonly used in literature to describe wake characteristics [8]. D. Wind velocity in a single wake The Jensen model assumes that the velocity deficit in the wake decays quadratically with the expansion of the wake. In [8] it is shown that the parameters of the Jensen model can be tuned to obtain a good fit of the time-averaged velocity profile in the far wake predicted by the SOWFA model for nonyawed conditions. An extension made in the model presented here needed to better fit the power data from Experiments and, is that the velocity deficit in the three wake zones decays quadratically with the distance from the rotor, rather than being directly related to the wake expansion. The velocity profile behind turbine j is modeled as: U w, j (x,r) = U j [ a j c j (x,r)] () with x, r the axial and lateral distances to the wake center, and with wake decay coefficient: c j, if r D w, j, / c c j (x,r) = j, if D w, j, / < r D w, j, / () c j, if D w, j, / < r D w, j, / if r > D w, j, / with the local wake decay coefficient for each zone given by: [ ] D j c j,q (x) =. () D j + k e m U,q (γ j )x Following a similar approach to the one used in Section III- A, the wake decay rates were adjusted for the rotor yaw angle by empirically deriving the following relationship between m U,q and γ i : m U,q (γ j ) = M U,q cos(a U + b U γ j ) for q =,, with parameters M U,q, a U, b U. (4) E. Combining wakes to find turbine-effective wind velocities Generally, we cannot assume the free-stream inflow into the wind plant to be known, but by inverting (), we can estimate the effective wind speeds at the front turbines using turbine power measurements. Then, the wind speeds at the downstream turbines can be estimated by combining the effect of the wakes, weighting the wake areas by their overlap with the rotors using the root-sum-square method of [4]. This results in the following formulations: U F denotes the set of upstream turbines located in the front that are not influenced by other turbines through wake interaction, and D = {i F i / U } denotes the set of turbines that is influenced by other turbines. Further, ĩ( j) denotes the index of a turbine in the set U that influences a turbine j D through its wake, and { x j j F } are the positions of the turbines along the wind. Then, the effective wind speeds at each turbine j F are estimated by: { f ( j) j U U j = (5) f ( j) j D with functions: f ( j) = [ P j / ρa j C P (a j,γ j ) ] /, f ( j) = Uĩ( j) X ( j) () with: X ( j) = i F :x i <x j [ a i q=c i,q (x j x i )min ( )] A ol i, j,q, A j (7) where A ol i, j,q denotes the overlapping area of different wake zones, see Figure b. These overlapping areas are calculated from the wake center and wake diameter predictions as described in Section III-B and III-C, using basic geometry. F. Fitting the wake parameters By fitting to the power data from T in Experiments and, the parameters for wake deflection, expansion, and decay were tuned manually (cf. Figure b, Table I). The results were validated by comparing the resulting wake velocity profiles for a single yawed turbine with the corresponding data generated by SOWFA in the experiments described in []; see Figure for this comparison. In our experience, the parameter k e is the most significant parameter when adjusting the model to different wind plant power data sets, measured at different atmospheric conditions, e.g., [9]. IV. WIND PLANT YAW OPTIMIZATION USING A GAME-THEORETIC APPROACH In this work, we used the game-theoretic (GT) approach of [9] to perform an optimization of the yaw settings in a wind plant based on the simplified model, and validated the results in SOWFA. The GT approach performs the optimization by making random perturbations to the yaw settings and holds the settings as a baseline setting if they yield an improvement of the wind plant total power, so as to iteratively find the global maximum of the wind plant total power. In Algorithm, the (simplified) optimization scheme of the GT approach is given as it is implemented in our simulations. The algorithm is somewhat different than the one presented in [9] in the way that the exploration distribution and the exploration rate are defined. Instead of choosing γ i randomly according to a uniform distribution over the full range of allowable values [ γ min,γ max], a normal distribution around the baseline setting γ i is used to choose the new setting γ i. Further, an annealing strategy is used: the probability of updating a yaw setting rather than keeping it the same as in the previous iteration, E, is reduced as the number of iterations increases, such that a higher density of perturbations results for the earlier iterations than for later iterations. This change was made to improve the convergence speed of the algorithm without losing the guarantee on convergence to the global optimum of the model.

5 Lateral distance [m] γ = 4 γ = 5 γ = γ = 5 γ = γ = 5 γ = γ = 5 γ = γ = 5 γ = γ = 5 γ = γ = 5 γ = γ = 5 γ = 4 8 wind speed [m/s] Fig. : Time-averaged wake velocity profiles at turbine hub-height at a 7D from the rotor, for different yaw angles of the rotor γ, as calculated with SOWFA (dashed) in the simulation described in [], and with the parametric model (solid). Algorithm The pseudocode below shows a GT approach for wind plant control, performing optimization of the yaw angles for increased electrical energy production. Index k denotes the iterations of the optimization. The variables γ i and P i are used to store past values of the control variables and the turbine powers, U denotes a uniform distribution, and N denotes a normal distribution, with σ as the standard deviation. : γ i i F : k : update P i i F using (5),() 4: P N i= P i (t) 5: γ i γ i : loop 7: k k + 8: update P i i F using (5),() 9: : if N i= P i (t) > P then γ i γ i i F : P N i= P i (t) : end if : for all i F do 4: R random value U (,) 5: E /βk τ : if R < E then 7: R random value N (, σ ) 8: γ i min ( max ( γ i + R,γ min),γ max) 9: else : γ i γ i : end if : end for : end loop V. YAW OPTIMIZATION SIMULATION STUDY We performed an evaluation of the parametric model and the GT optimization strategy on a wind plant consisting of two rows with three NREL 5-MW baseline turbines each, with a 5 rotor diameter (5D) spacing in the down-wind, and D in the cross-wind. First, the wind plant was simulated in SOWFA with greedy control settings for the yaw, i.e., the rotors were pointed into the of the mean wind inflow without any offset, yielding maximum power for the individual turbines. Then, we calculated the yaw settings that optimize the total wind plant production.8 x Total power, converged settings Total power, "greedy" settings Baseline Power, 5th 95th percentiles Baseline Power, 5th 75th percentiles Baseline Power, median iterations (a) Uniform distribution of the search actions.8 x Total power, converged settings Total power, "greedy" settings Baseline Power, 5th 95th percentiles Baseline Power, 5th 75th percentiles Baseline Power, median iterations (b) Normal distribution of the search actions, and annealing Fig. 4: GT optimization of the yaw settings of the x wind plant rotated with respect to wind, comparing the convergence of the baseline power ( P) when using uniform distribution to the approach with a normal distribution of the search actions and an annealing approach for adjusting the search rate. using the GT approach described in Section IV on the basis of the predictions given by the model presented in Section III. We performed a second SOWFA simulation with the optimized yaw settings, in which it is validated whether the electrical energy production improvement predicted by the simplified model is indeed achieved. Because of the high mesh and time resolution required ( cells,. s sample time), the computational cost of the CFD simulations is high: 59 hours of distributed computation on 5 processors, for a s simulated time. In Figure 4, we compare the convergence properties of the GT optimization using the uniform distribution of the search actions and an annealing strategy, with the GT approach using a uniform distribution of the search actions over the search range. In the normal distribution GT approach, the

6 search action distribution standard deviation is set as σ = 5, and the annealing parameters as β =.5, τ =. It is shown that a speed-up of the GT approach can be achieved by using the normal distribution with these settings. This may become more relevant if we develop a real-time implementation of the optimization algorithm on a large-scale wind plant. Each iteration of GT (a simulation of the steady-state of the wind plant with the parametric model) takes MATLAB about. ms to calculate on a. GHz PC. Figure 5b shows the results of the SOWFA simulations. It shows that after a period in which the wake develops and travels from one turbine to the next, the electrical energy production will decrease significantly in each of the cases because of wake interaction, but that the optimized yaw settings will reduce the wake interaction. The optimal yawing redirects the wake of upstream rotors away from downstream rotors (see also Figure 5a). This results in a % wind plant power increase with respect to the greedy case. The steadystate power predictions have a decent fit with the turbine powers predicted by the extended model. For these SOWFA simulations, an inflow with a % turbulence intensity and an 8 m/s mean velocity was used, which is the same inflow condition that was used in Experiments and. Note that a different spacing between the turbines in the wind was used in Experiments and to obtain the parametric model, namely 7D, and in that sense we used the model for extrapolation. The experiments were repeated with a 5 and rotation of the complete wind plant configuration with respect to the wind, cf. Figure 5c and 5d, to show the effect of wind changes on the wake interaction in the wind plant. For a rotation, there is far less to gain from the yaw optimization, because also in the greedy case there is little overlap of the wakes with the downstream turbines. This motivates the use of the parametric model as an internal model of a controller that adjusts the yaw settings to the wind. VI. CONCLUSIONS AND FUTURE WORK The parametric model presented in this paper can be used to optimize the turbine yaw settings in a wind plant, for increased total electrical energy production. In a highfidelity simulations of a small wind plant, we found that the model was be able to predict turbine powers for both the greedy and optimized settings, for changing configurations of the wind plant. Ongoing work includes implementing the extended model as an internal model for a wind plant controller that will continuously adjust the yaw reference settings to the wind online. As the inflow conditions (e.g., wind speed and turbulence intensity) change, the wake properties are affected, therefore the model parameters should be updated online. The parametric model presented in this paper has a relatively simple formulation, with a small number of parameters that can be identified using turbine power measurements. This low model complexity enables the development of such a fully data-driven approach for wind plant optimization control. Further ongoing research includes an alternative datadriven approach for the prediction of wake locations through machine-learning techniques based on available wind turbine measurements []. REFERENCES [] M. Steinbuch, W. de Boer, O. Bosgra, S. Peters, and J. Ploeg. Optimal control of wind power plants. Journal of Wind Engineering and Industrial Aerodynamics, vol. 7, pp. 7 4, 988. [] K. E. Johnson and N. Thomas. Wind farm control: addressing the aerodynamic interaction among wind turbines. Proceedings of the American Control Conference, St. Louis, USA, 9, pp [] J. Schepers and S. van der Pijl. Improved modelling of wake aerodynamics and assessment of new farm control strategies. 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7 mean flow 4 5 turbine greedy yaw: optimal yaw: turbine 4 greedy yaw: optimal yaw: 9.8 turbine greedy yaw: optimal yaw: turbine 5 greedy yaw: optimal yaw:.4 turbine greedy yaw: optimal yaw: turbine greedy yaw: optimal yaw:.4 (a) Hub-height velocity field in the rotated x wind plant with optimized yaw settings after 8 s of simulated time. total turbine greedy yaw: optimal yaw: turbine 4 greedy yaw: optimal yaw: turbine greedy yaw: optimal yaw: turbine 5 greedy yaw: optimal yaw:. 4 8 turbine greedy yaw: optimal yaw: turbine wakes develop power increase optimal vs. greedy yaw:.% greedy yaw: optimal yaw: (c) Power data x wind plant rotated 5 with respect to wind total wakes develop power increase optimal vs. greedy yaw: % (b) Power data x wind plant rotated with respect to wind total turbine greedy yaw: optimal yaw:. 4 8 turbine 4 greedy yaw: optimal yaw: turbine greedy yaw: optimal yaw: turbine 5 greedy yaw: optimal yaw:. 4 8 turbine greedy yaw: optimal yaw: turbine greedy yaw: optimal yaw: wakes develop power increase optimal vs. greedy yaw:.4% (d) Power data x wind plant rotated with respect to wind Fig. 5: In (a), a visualization of the SOWFA simulated flow field for the simulation of the rotated x wind plant, with optimal settings. In (b-d), SOWFA simulation power results (solid line) compared to the steady-state power predictions of the parametric model (dashed line) for both greedy and optimal settings. [] J. Jonkman, S. Butterfield, W. Musial, and G. Scott. Definition of a 5-MW Reference Wind Turbine for Offshore System Development. Technical report NREL/TP 5 8, 9. [] N. O. Jensen. A note on wind generator interaction. Technical report, Risø, 98. [4] I. Katic, J. Højstrup, and N. O. Jensen, A simple model for cluster efficiency. European Wind Energy Association Conference and Exhibition, 98, pp [5] A. Jiménez, A. Crespo, and E. Migoya. Application of a LES technique to characterize the wake deflection of a wind turbine in yaw. Wind Energy, vol., no., pp ,. [] F. D. Bianchi, H. D. Battista, and R. J. Mantz. Wind Turbine Control Systems; Principles, modelling and gain scheduling design. Springer- Verlag London, 7. [7] D. Medici. Experimental studies of wind turbine wakes: power optimisation and meandering. PhD dissertation, 5. [8] J. Annoni, P. Seiler, K. Johnson, P. Fleming, and P. Gebraad. Evaluating Wake Models for Wind Farm Control. American Control Conference, Portland, OR, USA, 4. [9] R. Barthelmie, S. Frandsen, K. Hansen, J. Schepers, K. Rados, W. Schlez, A. Neubert, L. E. Jensen, and S. Neckelmann. Modelling the impact of wakes on power output at Nysted and Horns Rev. Proceedings of the European Wind Energy Conference, Marseille, France, 9. [] P. Fleming, P. M. O. Gebraad, M. Churchfield, J. W. van Wingerden, A. Scholbrock, and P. Moriarty. Using particle filters to track wind turbine wakes for improved wind plant controls. American Control Conference, Portland, OR, USA, 4. 4